Is it possible to attach an object to the end of a curve and have the object point in the same direction as the end of the curve?
You can do it with a little trick.




Create the cube and the curve
Create a plane at the exact same position as the cube and scale it down so it is inside the cube. Do it in edit mode so that its object scale won't change
Parent the cube to the plane
Mark the plane as dupliface in the instancing section
Add a curve modifier to the plane


This is the start of the curve, though...

Edit: to do it at the end of the curve


Parent the cube to the curve
Set the curve as 'path animation' with only 1 frame
Adjust the cube orientation so that it fits the first control point of the curve